The high-pressure behaviour of ammonium metal formates has been investigated using high-pressure single-crystal X-ray diffraction on ammonium iron and nickel formates, and neutron powder diffraction on ammonium zinc formate in the pressure range of 0–2.3 GPa. A structural phase transition in the pressure range of 0.4–1.4 GPa, depending on the metal cation, is observed for all three ammonium metal formates. The hexagonal-to-monoclinic high-pressure transition gives rise to characteristic sixfold twinning based on the single-crystal diffraction data. Structure solution of the single-crystal data and refinement of the neutron powder diffraction characterise the pressure-induced distortions of the metal formate frameworks. The pressure dependence of the principal axes shows significantly larger anisotropic compressibilities in the high-pressure monoclinic phase (K1 = 48 TPa−1, K3 = −7 TPa−1) compared to the ambient hexagonal phase (K1 = 16 TPa−1, K3 = −2 TPa−1), and can be related to the symmetry-breaking distortions that cause deformation of the honeycomb motifs in the metal formate framework. While high-pressure Raman spectroscopy suggests that the ammonium cations remain dynamically disordered upon the phase transition, the pressure-induced distortions in the metal formate framework cause polar displacements in the ammonium cations. The magnitude of polarisation in the high-pressure phase of ammonium zinc formate was calculated based upon the offset of the ammonium cation relative to the anionic zinc formate framework, showing an enhanced polarisation of Ps ∼ 4 μC cm−2 at the transition, which then decreases with increasing pressure.